Analyzing the Point Multiplication Operation of Elliptic Curve Cryptosystem over Prime Field for Parallel Processing

The Elliptic Curve Cryptosystem shortly called as (ECC) is one of the asymmetric key cryptosystems, which provides a high security for wireless applications compared to other asymmetric key cryptosystem. The implementation of this algorithm over prime field Zp has a set of point operations, which are point addition, point subtraction, point multiplication, point division, point inversion, and point doubling. In these operations, the time complexity of the point multiplication is higher than any other time complexity of ECC point operations. So, it is necessary to find out an alternative implementation for point multiplication to take minimum amount of clock cycles, to reduce power consumption, and to support the software scheduling for parallel processing on arithmetic operations during execution. Considering this, the proposed implementation is very useful to perform encryption or decryption on texts, and also for analysing the strength of encryption or decryption computation